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3 years ago

Prove that the diagonals of a rhombus are perpendicular using coordinate geometry

Mathematics

1 answer:

lozanna [386]3 years ago

5 0

If we draw a rhombus OABC on a coordinate grid with one vertex at the point O (0,0)

and let its height be 1 then (using the Pythagoras theorem) the coordinates of the 4 points will be as follows:-

O = (0,0) , A = (1, 1), B = (sqrt2+ 1 , 1) , C = (sqrt2, 0)

Slope of the diagonal OB = 1 / (sqrt2 + 1)

Slope of the other diagonal AC = - 1 / (sqrt2 - 1)

Product of the slopes = - 1 / ( sqrt2 + 1)(sqrt2 - 1) = -1 / 1 = -1

This proves that the diagonals are perpendicular.

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3. Sam and Tim each have savings accounts. Every month they each put in some of their

Setler [38]

Answer:

$y = 30x +50$ --- Sam

$y = 20x +80$ --- Tim

Step-by-step explanation:

Given

Sam Tim

х --- f(x) --------------- g(x)

1 --- 80 --------------- 100

2 --- 110 --------------- 120

3 --- 140 --------------- 140

4 --- 170 -------------- 160

Required

Determine the y value

y value implies the equation of the table

Calculating the equation of Sam

First, we need to take any corresponding values of x and y

$(x_1,y_1) = (1,80)$

$(x_2,y_2) = (4,170)$

Next, we calculate the slope (m)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{170 - 80}{4 - 1}$

$m = \frac{90}{3}$

$m = 30$

Next, we calculate the line equation using:

$y - y_1=m(x-x_1)$

$y - 80 = 30(x - 1)$

$y - 80 = 30x - 30$

Make y the subject

$y = 30x - 30 + 80$

$y = 30x +50$

Calculating the equation of Tim

First, we need to take any corresponding values of x and y

$(x_1,y_1) = (1,100)$

$(x_2,y_2) = (4,160)$

Next, we calculate the slope (m)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{160 - 100}{4 - 1}$

$m = \frac{60}{3}$

$m = 20$

Next, we calculate the line equation using:

$y - y_1=m(x-x_1)$

$y - 100 = 20(x - 1)$

$y - 100 = 20x - 20$

Make y the subject

$y = 20x - 20+100$

$y = 20x +80$

7 0

3 years ago

What is the solution set? A.) (0, -2) B.) (2, 0) C.) (7, 0) D.) (5, 3)

max2010maxim [7]

Answer:

D.) (5, 3)

Step-by-step explanation:

Solution is where two lines intersect

Both lines intersect at x = 5 and y = 3

Answer

D.) (5, 3)

8 0

3 years ago

The diagram shows a square.

frosja888 [35]

Answer:

3.5 cm

Step-by-step explanation:

6x -1 = 4x + 6

2x = 7

x = 3.5

6 0

3 years ago

PLSSS HELPPPPP MEEEE I WILLL GIVVVEEE BRAINLIESTTTT!!!!!!

Ivenika [448]

Answer:

y = 3x - 9

Step-by-step explanation:

To write a line with a slope of 3, set the coefficient of x to be 3:

y = 3x

But notice, if we evaluate x when it is equal to 2, we get 2*3=6, but we want it to be -3. Therefore, we just subtract 9 from the equation:

y = 3x - 9

6 0

3 years ago

Help needed ASAP will give BRAINLIEST

dem82 [27]

Hourly pay of 18 dollars

5 0

3 years ago

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